# complex nrs determine polynomial from zeros of function

#### wortel

How do I determine the 4th degree polynomial with real coefficients from the following zeros of that function?
(i) and 2-3i.

#### Math Message Board tutor

How do I determine the 4th degree polynomial with real coefficients from the following zeros of that function?
(i) and 2-3i.
You are given the equivalent of:

0 + i $$\displaystyle \ \$$ and

2 - 3i

The other zeroes are their conjugates:

0 - i $$\displaystyle \ \$$ and

2 + 3i

x - i

x - (-i) = x + i

x - (2 - 3i)

x + (2 + 3i)

Multiply them together.

#### EvanJ

x + (2 + 3i)
Shouldn't that be x - (2 + 3i)? The other three roots were in the form x - something. I got the polynomial to be:

x^4 - 4x^3 + 14x^2 - 4x + 13

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